Does a plugin exist with this requirements ? WordPress

SOLVED

I need a plugin for bookings.

Description :

The user must be logged.
The user can book a gym class.
The number of places available appears.
If a user books a gym class for 10 personns, the message is something like "now there is 9 places available"

When a user books a class, a mail is send to this user and to the administrator (with the hours of the booking).

24 jours before the class, a reminder email is send to the user.

The user can change or delete his booking. In this case, the administrator and the user receive a new email with the new data.

Ok, but when you want to book an event, you open a post each time, no ? It's strange to book just a gym class.
It's not possible to book a gym class (for example) just toclick on the cell of the table ?

An ecommerce plugin with a more specific extension would be the best solution for the requirements you describe. I suggest woocommerce and the bookings extension: https://woocommerce.com/products/woocommerce-bookings/ that have all sorts of functions you require including bookings reminders, notifications, limitation on number of bookings and etc.

For change/delete booking i'm not sure but there is the basic functionality of "cancel order type".
Places available is a basic functionality of woocommerce just like with the show availability option for simple products ex. 6 in stock.

By "validated" and "deleted" I'm guessing you mean if the user purchases or cancels a subscription? If that's the case yes that's basic functionality of woocommerce , the administrator get notified whenever an order is placed or canceled so same goes with subscriptions